Besley: Chapter 7 Assignment 5

1
Besley Chapter 7Assignment 5

• Pg. 324 7-3 7-4
• Pg. 325 7-6
• Pg. 327 7-11

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Pg 324 7-3

• Your broker offers to sell you some shares of
  Wingler Co. common stock that paid a dividend
  of 2 yesterday. You expect the dividend to grow
  at the rate of five percent per year for the next
  three years, and if you buy the stock you plan to
  hold it for three years and then sell it.
• Find the expected dividend for each of the next
  three years that is, calculate D1, D2, and
  D3. Note that D0 2.

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Pg 324 7-3 continued

• Given that the appropriate discount rate is 12
  percent and that the first of these dividend
  payments will occur one year from now, find the
  present value of the dividend stream that is,
  calculate the PV of D1, D2, and D3, and then
  sum these PVs.
• PV 2.10(0.8929)2.21(0.7972)2.32(0.7118)
• 5.29

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Pg 324 7-3 continued

• You expect the price of the stock three years
  from now to be 34.73 that is you expect P3 to
  equal 34.73. Discount at a 12 percent rate,
  what is the present value of this expected future
  stock price? In other words, calculate the PV of
  34.73
• PV of P3 34.72(0.7118) 24.72

5
Pg 324 7-3 continued

• If you plan to buy the stock, hold it for three
  years, and then sell it for 34.73, what is the
  most you should pay for it?
• P0 24.72 5.29 30.01
• Use Equation 7-6 to calculate the present value
  of this stock. Assume that g 5, and it is
  constant.

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Pg 324 7-3 continued

• Is the value of this stock dependent upon how
  long you plan to hold it? In other words, if your
  planned holding period were two years or five
  years rather than three years, would this affect
  the value of the stock today, P0?
• The value of the stock is not dependent on the
  holding period, but rather is dependent on the
  cash flow stream.

7
Pg 324 7-4

• You buy a share of Damanpour Corporation stock
  for 21.40. You expect it to pay dividends of
  1.07, 1.1449, and 1.2250 in Years 1,2, and 3,
  respectively, and you expect to sell it at a
  price of 26.22 at the end of three years.
• Calculate the growth rate in dividends.
• g1 (1.1449-1.07)/1.07 7
• g2 1.2250/1.1449 1.0 7

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Pg 324 7-4 continued

• Calculate the expected dividend yield.
• 1.07/21.40 5
• Assuming that the calculated growth rate is
  expected to continue, you can add the dividend
  yield to the expected growth rate to get the
  expected total rate of return. What is this
  stocks expected total rate of return?

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Pg 325 7-6

• Bayboro Sails is expected to pay dividends of
  2.50, 3.00, and 4.00 in the next three
  years-D1, D2, and D3, respectively. After
  three years, the dividend is expected to grow at
  a constant rate equal to four percent per year
  indefinitely. Stockholders require a return of
  14 to invest in the common stock of Bayboro
  Sails.

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Pg 325 7-6 continue

• Compute the present value of the dividends
  Bayboro is expected to pay over the next three
  years.
• PV 2.50(0.8772) 3.00(0.7695)
  4.00(0.6750)
• 7.20
• For what price should investors expect to be able
  to sell the common stock of Bayboro at the end of
  three years? (Hint The dividend will grow at a
  constant 4 percent in Year 4, Year 5, and every
  year thereafter, so Equation 7-6 can be used to
  find P3-the appropriate dividend to use in the
  numerator is D4.)

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Pg 325 7-6 continue

• Compute the value of Bayboros common stock
  today, P0.

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Pg 327 7-11

• Suppose Sartoris Chemical Companys management
  conducts a study and concludes that if Sartoris
  expanded its consumer products division (which is
  less risky that its primary business, industrial
  chemicals), the firms beta would decline from
  1.2 to 0.9. However, consumer products have a
  somewhat lower profit margin, and this would
  cause Sartoriss constant growth rate in earnings
  and dividends to fall from seven to five percent.

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Pg 327 7-11 continued

• Should management make the change? Assume the
  following km 12 krf 9 D0 2.

ks NEW kRF (ks-kRF)bs 9(12-9)0.9
11.7
ks OLD kRF (ks-kRF)bs 9(12-9)1.2
12.6
P0NEW 2(1.05)/(.117-.05)
P0OLD 2(1.07)/(.126-.07)
31.34
38.21
Since the New price is lower than the Old price,
the expansion into the less risky consumer
products market.
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Pg 327 7-11 continued

• Assume all the facts as given above expect the
  change in the beta coefficient. How low would
  the beta have to fall to cause the expansion to
  be a good one? (Hint Set P0 under the new
  policy equal to P0 under the old one, and find
  the new beta that will produce this equality.

Solve for ks
2.10 38.21(ks)-1.9105
4.0105 38.21(ks)
ks 0.10496
Solve for bs
10.496 9 3(bs)
1.496 3(bs)
bs 0.49865